Go figure

An expression used after a counter-intuitive statement to indicate that the speaker/writer doesn't understand or necessarily agree with the statement. Think of it as the textual equivalent of a heck-if-I-know shrug.

If I were to take a stab at it's literal meaning, I'd say it's an invitation for the listener to get to the bottom of the apparent incongruence. It could be inferred that the speaker/writer is tired of thinking about it.